Certain embodiments described herein generally relate to imaging techniques. More specifically, certain aspects pertain to Fourier ptychographic imaging methods that implement an embedded pupil function recovery technique.
Imaging lenses ranging from microscope objectives to satellite-based cameras are physically limited in the total number of features they can resolve. These limitations are a function of the point-spread function (PSF) size of the imaging system and the inherent aberrations across its image plane field of view (FOV). Referred to as the space-bandwidth product, the physical limitation scales with the dimensions of the lens but is usually on the order of 10 megapixels regardless of the magnification factor or numerical aperture (NA). A discussion of space-bandwidth product of conventional imaging systems can be found in Lohmann, A. W., Dorsch, R. G., Mendlovic, D., Zalevsky, Z. & Ferreira, C., “Space—bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A. 13, pages 470-473 (1996), which is hereby incorporated by reference for this discussion. While conventional imaging systems may be able to resolve up to 10 megapixels, there is typically a tradeoff between PSF and FOV. For example, certain conventional microscope objectives can offer a sharp PSF (e.g., 0.5 μm) across a narrow FOV (e.g., 1 mm), while others imaging systems with wide-angle lenses can offer a wide FOV (e.g., 10 mm) at the expense of a blurry PSF (e.g., 5 μm).
Certain interferometric synthetic aperture techniques that try to increase spatial-bandwidth product are described in Di, J. et al., “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning,” Appl. Opt. 47, pp. 5654-5659 (2008); Hillman, T. R., Gutzler, T., Alexandrov, S. A., and Sampson, D. D., “High-resolution, wide-field object reconstruction with synthetic aperture Fourier holographic optical microscopy,” Opt. Express 17, pp. 7873-7892 (2009); Granero, L., Micó, V., Zalevsky, Z., and Garcia, J., “Synthetic aperture superresolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information,” Appl. Opt. 49, pp. 845-857 (2010); Kim, M. et al., “High-speed synthetic aperture microscopy for live cell imaging,” Opt. Lett. 36, pp. 148-150 (2011); Turpin, T., Gesell, L., Lapides, J., and Price, C., “Theory of the synthetic aperture microscope,” pp. 230-240; Schwarz, C. J., Kuznetsova, Y., and Brueck, S., “Imaging interferometric microscopy,” Optics letters 28, pp. 1424-1426 (2003); Feng, P., Wen, X., and Lu, R., “Long-working-distance synthetic aperture Fresnel off-axis digital holography,” Optics Express 17, pp. 5473-5480 (2009); Mico, V., Zalevsky, Z., Garcia-Martinez, P., and Garcia, J., “Synthetic aperture superresolution with multiple off-axis holograms,” JOSA A 23, pp. 3162-3170 (2006); Yuan, C., Zhai, H., and Liu, H., “Angular multiplexing in pulsed digital holography for aperture synthesis,” Optics Letters 33, pp. 2356-2358 (2008); Mico, V., Zalevsky, Z., and Garcia, J., “Synthetic aperture microscopy using off-axis illumination and polarization coding,” Optics Communications, pp. 276, 209-217 (2007); Alexandrov, S., and Sampson, D., “Spatial information transmission beyond a system's diffraction limit using optical spectral encoding of the spatial frequency,” Journal of Optics A: Pure and Applied Optics 10, 025304 (2008); Tippie, A. E., Kumar, A., and Fienup, J. R., “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express 19, pp. 12027-12038 (2011); Gutzler, T., Hillman, T. R., Alexandrov, S. A., and Sampson, D. D., “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett. 35, pp. 1136-1138 (2010); and Alexandrov, S. A., Hillman, T. R., Gutzler, T., and Sampson, D. D., “Synthetic aperture Fourier holographic optical microscopy,” Phil. Trans. R. Soc. Lond. A 339, pp. 521-553 (1992), all of which are hereby incorporated by reference for the discussion of attempts to increase spatial bandwidth. Most of the above-described interferometric synthetic aperture techniques include setups that record both intensity and phase information using interferometric holography such as off-line holography and phase-shifting holography. Interferometric holography has its limitations. For example, interferometric holography recordings typically use highly coherent light sources. As such, the constructed images typically suffer from coherent noise sources such as speckle noise, fixed pattern noise (induced by diffraction from dust particles and other optical imperfections in the beam path), and multiple interferences between different optical interfaces. Thus the image quality is typically worse than from a conventional microscope. On the other hand, using off-axis holography sacrifices spatial-bandwidth product (i.e., reduces total pixel number) of the image sensor. A discussion of certain off-axis holography methods can be found in Schnars, U. and Jüptner, W. P. O., “Digital recording and numerical reconstruction of holograms,” Measurement Science and Technology, 13, R85 (2002), which is hereby incorporated by reference for this discussion. In addition, interferometric imaging techniques may subject to uncontrollable phase fluctuations between different measurements. Hence, accurate a priori knowledge of the sample location may be needed to set a reference point in the image recovery process. Another limitation is that many of these interferometric imaging systems require mechanical scanning to rotate the sample and thus precise optical alignments, mechanical control at a sub-micron level, and associated maintenances are required by these systems. In terms of spatial-bandwidth product, these interferometric imaging systems may present little to no advantage as compared with a conventional microscope.
Previous lensless microscopy such as in-line holography and contact-imaging microscopy also present drawbacks. For example, conventional in-line holography does not work well with contiguous samples and contact-imaging microscopy requires a sample to be in close proximity to the sensor. A discussion of certain digital in-line holography devices can be found in Denis, L., Lorenz, D., Thiebaut, E., Fournier, C. and Trede, D., “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, pp. 3475-3477 (2009); Xu, W., Jericho, M., Meinertzhagen, I., and Kreuzer, H., “Digital in-line holography for biological applications,” Proc. Natl Acad. Sci. USA 98, pp. 11301-11305 (2001); and Greenbaum, A. et al., “Increased space—bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, page 1717 (2013), which are hereby incorporated by reference for this discussion. A discussion of certain contact-imaging microscopy can be found in Zheng, G., Lee, S. A., Antebi, Y., Elowitz, M. B. and Yang, C., “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl Acad. Sci. USA 108, pp. 16889-16894 (2011); and Zheng, G., Lee, S. A., Yang, S. & Yang, C., “Sub-pixel resolving optofluidic microscope for on-chip cell imaging,” Lab Chip 10, pages 3125-3129 (2010), which are hereby incorporated by reference for this discussion.
A high spatial-bandwidth product is very desirable in microscopy for biomedical applications such as pathology, haematology, phytotomy, immunohistochemistry, and neuroanatomy. For example, there is a strong need in biomedicine and neuroscience to image large numbers of histology slides for evaluation. This need has prompted the development of sophisticated mechanical scanning and lensless microscopy systems. These systems increase spatial-bandwidth product using complex mechanisms with high precision to control actuation, optical alignment, and motion tracking. These complex mechanisms tend to be expensive to fabricate and difficult to use and maintain.